{"title":"A minimax theorem for locally Lipschitz functionals and applications","authors":"Marcelo F. Furtado, João Pablo P. Da Silva","doi":"10.1007/s11854-024-0346-z","DOIUrl":null,"url":null,"abstract":"<p>We prove an abstract theorem which provides multiple critical points for locally Lipschtiz functionals under the presence of symmetry. The abstract result is applied to find multiple solutions in <i>H</i><span>\n<sup>1</sup><sub>0</sub>\n</span> (Ω) for the critical semi-linear elliptic equation − Δ<i>u</i> = <i>f</i>(<i>x, u</i>) + ∣<i>u</i>∣<sup>4/(<i>N</i>−2)</sup><i>u</i>, where <i>f</i> is a discontinuous perturbation and Ω ⊂ ℝ<sup><i>N</i></sup> is a bounded smooth domain.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal d'Analyse Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11854-024-0346-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove an abstract theorem which provides multiple critical points for locally Lipschtiz functionals under the presence of symmetry. The abstract result is applied to find multiple solutions in H10 (Ω) for the critical semi-linear elliptic equation − Δu = f(x, u) + ∣u∣4/(N−2)u, where f is a discontinuous perturbation and Ω ⊂ ℝN is a bounded smooth domain.
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